The perimeter of right triangle ABC is equal to the perimeter of isosceles triangle DEF. The lengths of the legs of the right triangle are 6 and 8. If the length of each side of the isosceles triangle is an integer, what is the greatest possible length for one of the sides of isosceles triangle DEF?

They tell you that the legs of the right triangle are 6 and 8. It is obvious that the height of the triangle would be the 6, and the length would be the 8. With the given numbers 6 and 8, you can tell that we are going to be increasing by 2, which is where we get the 10 from on the slanted side of the right triangle. The perimeter of the right triangle is 24. We know this because we added all of the sides together. Half of 24 is 12, so we know that the isosceles triangle has to be less than 12. Two of the sides of the isosceles triangle have to be the same, and that is why it would be 11, 11, 2.

Which of the following correctly classifies the triangle?
A. The triangle is an acute isosceles triangle.
B. The triangle is an acute equilateral triangle.
C. The triangle is a right isosceles triangle.
D. The triangle is an acute scalene triangle.

Answer This Question

First Name:

School Subject:

Answer:

Related Questions

geometry - The perimeter of right triangle RST is equal to the perimeter of ...

geometry - triangle abc is similar to def, the lengths of the sides of triangle ...

Math - If all of the following triangles have the same perimeter, which has the ...

geometry - In similar triangles ABC and DEF, corresponding sides AB and DE equal...

geometry - In the accompanying diagram, triangle ABCis similar to triangle DEF...

math - The base of an isosceles triangle is four less than the sum of the ...

geometry - The perimeter of an isosceles triangle is 37 in. The lengths of the ...

geometry - Triangle ABC is similar to triangle DEF. The sides of ABC are 5,8 and...

Math - 1) The hypotenuse of an isosceles right triangle is 8 cm longer than ...

Math - If triangle ABC is similar to triangle DEF and the perimeter of ABC is 4 ...